Question: Simplify the following expression: $z = \dfrac{-24t}{48t + 132}$ You can assume $t \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-24t = - (2\cdot2\cdot2\cdot3 \cdot t)$ The denominator can be factored: $48t + 132 = (2\cdot2\cdot2\cdot2\cdot3 \cdot t) + (2\cdot2\cdot3\cdot11)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $z = \dfrac{(12)(-2t)}{(12)(4t + 11)}$ Dividing both the numerator and denominator by $12$ gives: $z = \dfrac{-2t}{4t + 11}$